Solitary Waves in Dispersive Complex Media
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"Solitary Waves in Dispersive Complex Media" by Vasily Y. Belashov, Sergey V. Vladimirov is a mathematics book and learning resource focused on Dynamics. Best for teachers, students, and readers looking for stronger mathematical understanding.
This book is devoted to one of the most interesting and rapidly developing areas of modern nonlinear physics and mathematics – theoretical, analytical andnumerical,studyofthestructureanddynamicsofone-dimensionalaswell as two- and three-dimensional solitons and nonlinear wave packets described by the Korteweg–de Vries (KdV), Kadomtsev–Petviashvili (KP), nonlinear Schr ̈ odinger (NLS) and derivative nonlinear Schr ̈ odinger (DNLS) classes of equations. Special attention is paid to generalizations (relevant to various complex physical media) of these equations, accounting for higher-order d- persion corrections, in?uence of dissipation, instabilities, and stochastic ?- tuations of the wave ?elds. We present here a coordinated approach to the theory, simulations, and applications of the nonlinear one-, two-, and three-dimensional solitary wave solutions. Overall, the content of the book is a systematic account of results notonlyalreadyknownintheliterature,butalsothoseofneworiginalstudies related to the theory of models allowing soliton solutions, and analyses of the stability and asymptotics of these solutions. We give signi?cant consideration to numerical methods and results of numerical simulations of the structure and dynamics of solitons and nonlinear wave packets. Together with deep insights into the theory, applications to various branches of modern physics are considered, especially to plasma physics (such as space plasmas including ionospheric and magnetospheric processes), hydrodynamics, and atmosphere dynamics. Presently,thetheoryofone-dimensionalnonlinearequationsoftheclasses consideredbytheauthorsiswelldeveloped,andtheprogressinstudiesofthe structure and evolution of one-dimensional solitons and wave packets is ob- ous. This progress was especially fast after the discovery of hidden algebraic symmetries of the KdV, NLS, and other (integrable by the inverse scatt- ing transform (IST) method) classes of one-dimensional evolution equations.
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"Solitary Waves in Dispersive Complex Media" by Vasily Y. Belashov, Sergey V. Vladimirov is a mathematics book and learning resource focused on Dynamics. Best for teachers, students, and readers looking for stronger mathematical understanding.
Topic: Dynamics
Author: Vasily Y. Belashov, Sergey V. Vladimirov
Who this is for:
- Teachers and classroom instructors
- Students building subject mastery
- Readers looking for practical learning support
Why this book matters: It stands out as a practical math resource that helps explain concepts, strengthen problem-solving, and support classroom or independent learning.
This book is devoted to one of the most interesting and rapidly developing areas of modern nonlinear physics and mathematics – theoretical, analytical andnumerical,studyofthestructureanddynamicsofone-dimensionalaswell as two- and three-dimensional solitons and nonlinear wave packets described by the Korteweg–de Vries (KdV), Kadomtsev–Petviashvili (KP), nonlinear Schr ̈ odinger (NLS) and derivative nonlinear Schr ̈ odinger (DNLS) classes of equations. Special attention is paid to generalizations (relevant to various complex physical media) of these equations, accounting for higher-order d- persion corrections, in?uence of dissipation, instabilities, and stochastic ?- tuations of the wave ?elds. We present here a coordinated approach to the theory, simulations, and applications of the nonlinear one-, two-, and three-dimensional solitary wave solutions. Overall, the content of the book is a systematic account of results notonlyalreadyknownintheliterature,butalsothoseofneworiginalstudies related to the theory of models allowing soliton solutions, and analyses of the stability and asymptotics of these solutions. We give signi?cant consideration to numerical methods and results of numerical simulations of the structure and dynamics of solitons and nonlinear wave packets. Together with deep insights into the theory, applications to various branches of modern physics are considered, especially to plasma physics (such as space plasmas including ionospheric and magnetospheric processes), hydrodynamics, and atmosphere dynamics. Presently,thetheoryofone-dimensionalnonlinearequationsoftheclasses consideredbytheauthorsiswelldeveloped,andtheprogressinstudiesofthe structure and evolution of one-dimensional solitons and wave packets is ob- ous. This progress was especially fast after the discovery of hidden algebraic symmetries of the KdV, NLS, and other (integrable by the inverse scatt- ing transform (IST) method) classes of one-dimensional evolution equations.
| Author | Vasily Y. Belashov, Sergey V. Vladimirov |
| Publisher | Springer |
| Published | 2010-10-19 |
| ISBN-13 | 9783642062407 |
| Binding | Paperback |
| Pages | 294 |
| Language | English |
| Subjects | Science |
| Topic | Dynamics |
| Series | Springer Solid-State Sciences |
Format: Paperback
Length: 294 pages
Language: English
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